Apparently they are not truly clay. They are in fact grey floor tiles that Leo used: just punched the dots out of cheap old floor tiles! So I would guess that they are quite resistant to staining beyond the surface.
Try this, put a dab of WD40 on a paper towel and rub a dot to see if it lifts the surface stain. If not I would dry polish he entire neck with a scotchbrite pad and see if it rubs surface stains off. Then oil the neck to hydrate the rosewood. Cleaning the rosewood and dots won't hurt value.
'73-4 Ampeg V4B, Ampeg PF350,PF115HE, PF115LF, 115 Traynor, 1962 Fender Jazz, 75 Gibson G3, '10 Squier VM Jazz, Squier CV 60's P Sonic, Squier CV 50's P blonde, Epiphone Thunderbird IV